Problem: Simplify the following expression: $r = \dfrac{10}{6q + 8} \div \dfrac{8}{4q}$
Explanation: Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{10}{6q + 8} \times \dfrac{4q}{8}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 10 \times 4q } { (6q + 8) \times 8}$ $r = \dfrac{40q}{48q + 64}$ Simplify: $r = \dfrac{5q}{6q + 8}$